Evidence for a constant IMF in early-type galaxies based on their X-ray binary populations
Mark B. Peacock, Stephen E. Zepf, Thomas J. Maccarone, Arunav Kundu, Anthony H. Gonzalez, Bret D. Lehmer, Claudia Maraston
aa r X i v : . [ a s t r o - ph . GA ] F e b Draft version November 29, 2017
Preprint typeset using L A TEX style emulateapj v. 5/2/11
EVIDENCE FOR A CONSTANT IMF IN EARLY-TYPE GALAXIES BASED ON THEIR X-RAY BINARYPOPULATIONS †‡ Mark B. Peacock , Stephen E. Zepf , Thomas J. Maccarone , Arunav Kundu , , Anthony H. Gonzalez ,Bret D. Lehmer , , Claudia Maraston , Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA; [email protected] Texas Tech University, Physics Department, Box 41051, Lubbock, TX 79409, USA Eureka Scientific, Inc., 2452 Delmer Street, Suite 100 Oakland, CA 94602, USA Tata Institute of Fundamental Research, Homi Bhabha Rd, Mumbai 400005, India Department of Astronomy, University of Florida, Gainesville, FL 32611, USA The Johns Hopkins University, Homewood Campus, Baltimore, MD 21218, USA NASA Goddard Space Flight Center, Code 662, Greenbelt, MD 20771, USA Institute of Cosmology and Gravitation, Dennis Sciama Building, Burnaby Road, Portsmouth PO1 3FX, UK and Draft version November 29, 2017
ABSTRACTA number of recent studies have proposed that the stellar initial mass function (IMF) of early typegalaxies varies systematically as a function of galaxy mass, with higher mass galaxies having bottomheavy IMFs. These bottom heavy IMFs have more low-mass stars relative to the number of highmass stars, and therefore naturally result in proportionally fewer neutron stars and black holes. Inthis paper, we specifically predict the variation in the number of black holes and neutron stars basedon the power-law IMF variation required to reproduce the observed mass-to-light ratio trends withgalaxy mass. We then test whether such variations are observed by studying the field low-mass X-raybinary populations (LMXBs) of nearby early-type galaxies. In these binaries, a neutron star or blackhole accretes matter from a low-mass donor star. Their number is therefore expected to scale withthe number of black holes and neutron stars present in a galaxy. We find that the number of LMXBsper K-band light is similar among the galaxies in our sample. These data therefore demonstrate theuniformity of the slope of the IMF from massive stars down to those now dominating the K-bandlight, and are consistent with an invariant IMF. Our results are inconsistent with an IMF which variesfrom a Kroupa/Chabrier like IMF for low mass galaxies to a steep power-law IMF (with slope x =2.8)for high mass galaxies. We discuss how these observations constrain the possible forms of the IMFvariations and how future Chandra observations can enable sharper tests of the IMF.
Subject headings: stars: luminosity function, mass function - galaxies: stellar content - galaxies:elliptical and lenticular, cD - X-rays: binaries INTRODUCTION
The stellar initial mass function (IMF) describes theinitial distribution of masses when a population of starsformed. The IMF is of fundamental importance to awide range of astrophysics. Unfortunately, it is very dif-ficult to directly measure the IMF for external galaxies,and our knowledge of the IMF is primarily based on thestudies of the Milky Way (MW), where the stellar pop-ulation can be directly measured to low stellar masses(e.g. Kroupa 2001; Chabrier 2003). Written as a differen-tial mass function, dN/dm ∝ m − x , the Kroupa GalacticIMF has a Salpeter-like slope of x =2.3 (Salpeter 1955)for stars more massive than 0 . M ⊙ and a flatter slopeof x =1.3 for stars with masses between 0.5 M ⊙ and 0.08 M ⊙ . The Chabrier log-normal representation of the IMFis very similar. Studies of the MW’s IMF have shown it † Based in part on observations made with the NASA/ESA
Hubble Space Telescope , and obtained from the Hubble LegacyArchive, which is a collaboration between the Space TelescopeScience Institute (STScI/NASA), the Space Telescope EuropeanCoordinating Facility (ST-ECF/ESA) and the Canadian Astron-omy Data Centre (CADC/NRC/CSA). ‡ The scientific results reported in this article are based in parton data obtained from the
Chandra
Data Archive and observa-tions made by the
Chandra
X-ray Observatory and publishedpreviously in cited articles. to be generally invariant (see e.g. Bastian et al. 2010) anda universal IMF, based on the MW’s stellar population,is commonly assumed. However, in extragalactic studiessome recent evidence suggests that the IMF may not beuniversal.One method for investigating the ratio of low to highmass stars in unresolved stellar populations is to lookat the strength of gravity-sensitive features in their inte-grated spectra (e.g. Cohen 1978; Faber & French 1980;Carter et al. 1986; Couture & Hardy 1993). Some suchstudies have found that the strengths of the giant sen-sitive Ca ii triplet indices decrease (Saglia et al. 2002;Cenarro et al. 2003) and the dwarf sensitive Na i doubletand Wing-Ford molecular FeH band absorption featuresincrease (van Dokkum & Conroy 2010, 2011) with galaxyvelocity dispersion. These observations, and full spectralfitting to stellar population models, have led to a numberof papers suggesting that the IMF may become increas-ingly bottom heavy as the luminosity and velocity disper-sion of the galaxy increases (Conroy & van Dokkum 2012;Ferreras et al. 2013; La Barbera et al. 2013). Specifically,these papers find that lower mass elliptical galaxies havespectra consistent with a Kroupa like IMF (as seen inthe MW), while galaxies at the high mass end requirea steeper IMF, with slopes up to x ≃ M/L for early-type galaxies increases systemat-ically with increasing galaxy mass, luminosity, and veloc-ity dispersion. The reason for this relationship has beeninvestigated by many studies, with two mechanisms gen-erally proposed (e.g. Renzini & Ciotti 1993; Zepf & Silk1996; Treu et al. 2010; Graves & Faber 2010; Cappellariet al. 2012). The first, is that higher velocity dispersiongalaxies could have systematically larger fractions of darkmatter in the inner regions. The alternative, is that theIMF may vary, with higher luminosity and larger velocitydispersion galaxies having a systematically larger
M/L ratio because of systematic changes in the IMF. Cappel-lari et al. (2012) proposed, based on their detailed dy-namical investigation, that the dark matter variationscan not explain the observed
M/L variations. Theirconclusion is that variations in the IMF are required toexplain the observed
M/L variations, with high massgalaxies having either a relatively top heavy IMF (witha slope x =1.5, due to relatively more stellar remnantscontributing to the mass of the galaxy, but little to itslight) or a relatively bottom heavy IMF (with a slope x =2.8, due to relatively more low mass stars, which havehigher M/L ratios). The kinematic results cannot dis-tinguish between these two cases, but are consistent withthe bottom heavy IMF proposed from the absorption linestudies cited above.Further evidence for a bottom heavy IMF in massivegalaxies comes from some gravitational lensing studies.Treu et al. (2010) studied 56 gravitational lenses andfound that their inferred masses relative to those pre-dicted from stellar population fits increased as a functionof the galaxy’s velocity dispersion. They tentatively con-clude that this may be due to a steepening of the IMFas a function of galaxy mass. However, not all gravita-tional lensing results agree with a bottom heavy IMF inhigh mass galaxies. In particular, Smith & Lucey (2013)recently studied the closest known strong-lensing galaxy,the giant elliptical ESO325-G004. This galaxy has a highvelocity dispersion and features a strong (dwarf star sen-sitive) Na I 8200˚A spectral feature. However, the inferredmass to light ratio for this massive galaxy is consistentwith that predicted from stellar population models witha standard Kroupa IMF and inconsistent with a Salpeter(or steeper) IMF.For very low mass galaxies, direct observations of thestellar populations in two of the Milky Way’s dwarfspheroidal satellite galaxies suggests that they have aflatter than Kroupa IMF (with x =1.2 for Hercules and x =1.3 for Leo IV; Geha et al. 2013). Given the very lowmass of these galaxies, this result is consistent with the proposed flattening of the IMF with decreasing galaxymass. A flat IMF may even extend to the very lowmass ultracompact dwarf galaxies (UCDs). Some UCDsare observed to have high M/L ratios that could be ex-plained by them having either a relatively flat IMF or adark matter component (e.g. Ha¸segan et al. 2005; Mieskeet al. 2008; Mieske & Kroupa 2008). Dabringhausen et al.(2012) also proposed that UCDs may host more low massX-ray binaries (LMXBs) than expected. If this is thecase, it would be consistent with the higher fraction ofstellar remnants that are produced by a flatter IMF.In this paper, we search for an independent signatureof a variation in the IMF with galaxy mass. In particular,we probe the high mass end of the stellar populations inthese galaxies, based on their field LMXB populations.These binaries consist of a black hole (BH) or a neu-tron star (NS) accreting from a low mass donor star andhence track the population of massive stars that formedin a galaxy. The proposed variation of a galaxy’s IMFfrom a Kroupa IMF at low mass to an x =2.8 IMF athigh mass therefore predicts relatively fewer LMXBs perstellar mass in higher mass galaxies. In Section 2 we dis-cuss the galaxies studied in this paper and the archivedoptical and X-ray data used. In Section 3, we present thepopulation of field LMXBs in these galaxies. Finally, inSection 4 we predict how the LMXB population shouldvary as a function of mass due to a variable IMF and testthese predictions against the observed populations. GALAXY SAMPLE & DATA
To investigate the LMXB populations of local galax-ies, we select a sample of galaxies based on the followingcriteria: (1) they are early type galaxies with little on-going star formation and thought to have similarly oldstellar populations (see e.g. Trager et al. 2000; Terlevich& Forbes 2002; S´anchez-Bl´azquez et al. 2006; Sil’chenko2006; Thomas et al. 2010, and Section 4.3); (2) theyhave precise dynamical mass estimates from Cappellariet al. (2012), Gebhardt et al. (2007, NGC 4594) or Jardelet al. (2011, NGC 1399); (3) they have deep X-ray ob-servations from the
Chandra observatory, so that theirLMXB populations can be reliably measured; (4) theyhave optical photometry from
Hubble Space Telescope ( HST ) advanced camera for surveys (ACS) mosaics cov-ering most of the galaxy’s optical emission. We excludeM 87 from this sample due to concerns over accuratelymeasuring its LMXB population against the high back-ground from the hot gas that makes up its interstellarmedium. The resulting sample of galaxies is shown inTable 1. It can be seen that the galaxies span only asmall range of colors. The sample includes the bright-est cluster galaxies, NGC 4472 and NGC 1399 (also thecentral dominant galaxy in the Fornax cluster). Thesebrightest galaxies are where the extremely bottom heavyIMF’s have been previously proposed (van Dokkum &Conroy 2010). The galaxies then span a range of K-bandluminosities ( L K ), down to lower mass galaxies that arethought to have Kroupa like IMFs, with L K varying from2 − × L K, ⊙ . The sample therefore probes the rangeof masses over which significant variations in the IMFshould be present (if such variations exist). X-ray data/ catalogs esting for variability in the IMF at high stellar masses 3
TABLE 1Galaxy sample
Name type i dist. ii ref ii S iii N log( σ ) iv ref iv r v inner r vi ext e vi M Kvi (J-K) vi NGC... Mpc kms − arcsec arcsec4649 E2 16.5 2 6.7 2.488 1 15 241.3 0.19 -25.26 0.9394472 E2 16.7 2 5.6 2.460 1 15 313.4 0.19 -25.61 0.8831399 E1 20.0 1 12.4 2.447 2 10 202.2 0.00 -25.19 0.9244594 SA 9.0 3 2.0 2.400 3 22.5* 297.1 0.46 -24.76 0.9934278 E1-2 16.1 1 6.9 2.358 1 10 155.0 0.07 -23.76 0.9153379 E1 10.6 1 1.2 2.294 1 10 191.7 0.15 -23.53 0.9074697 E6 11.7 1 2.5 2.256 1 10 240.2 0.37 -23.85 0.8807457 SA0 13.2 4 3.1 1.870 1 5 155.1 0.45 -22.43 0.890Properties of the galaxies studied in this paper, sorted by decreasing σ . i from de Vaucouleurs et al. (1991); ii distances in Mpc fromsurface brightness fluctuation measurements from: (1) Blakeslee et al. (2001); (2) Blakeslee et al. (2009); (3) Jensen et al. (2003);(4) Tonry et al. (2001); iii Globular cluster specific frequency from Ashman & Zepf (1998) and Hargis et al. (2011, for NGC 7457); iv galaxy’s velocity dispersion from: (1) Cappellari et al. (2012); (2) Saglia et al. (2000); (3) Jardel et al. (2011); v The radius defining thecentral region that is excluded from our analysis *For NGC 4594 we remove an elliptical inner region with semi-minor axis = 22.5 ′′ andsemi-major axis = 168 ′′ ; vi Galaxy data from the two micron all sky survey (2MASS) large galaxy atlas (LGA) (Jarrett et al. 2003), ‘to-tal’ extrapolated galaxy semi-major axis (r ext ), K s -band ellipticity ( e = 1 − b/a ), K s -band magnitude within this ellipse (M K ) and J-K s color TABLE 2Galaxy data and X-ray source populations
HST
ACS data i Chandra data ii Galaxy light iii
Number of X-ray sources iv Name blue filter red filter No. exp. time 90% limit ref covered N x , field N x , GCs N x , back NGC... ksec × ergs − L K , cov / L K , ext i The number of different
HST /ACS fields used to identify optical counterparts to X-ray sources (No.) and the filters used. *For NGC 7457,only WFPC2 observations were available, the blue and red filters listed cover different regions of the galaxy, so allow source identification,but not color information; ii Chandra data used to study the galaxy. Quoted are the total exposure times, estimated 90% completenesslimits and references for the X-ray catalog used. X-ray source catalog references are: (1) Paolillo et al. (2011); (2) Brassington et al.(2008); (3) Brassington et al. (2009); (4) Joseph (2013); (5) Li et al. (2010); (6) Luo et al. (2013); (7) Sivakoff et al. (2008); (8) G¨ultekinet al. (2012); iii
The fraction of the galaxy’s stellar light covered by this study (relative to M K , quoted in Table 1); iv The number of X-raysources: with no optical counterparts (N x , field ); associated with globular cluster (GC) like counterparts (N x , GCs ); and associated withother optical counterparts (N x , back ). The total
Chandra exposure times and associated de-tection limits for these galaxies are quoted in Table 2.Most of the galaxies have long combined exposures ofover 100ks. We also include the galaxy NGC 7457, whichhas a shorter exposure time of 30ks. This galaxy is ofparticular interest to our study because its relatively lowmass should result in a large effect on its LMXB popu-lation, if the IMF relationship is present. These data al-low the X-ray populations of these galaxies to be studieddown to detection limits of L x = 3 × − × ergs − (where these limits are the 90% completeness limits thatwere determined by the studies referenced in Table 2).This is deep enough to allow accurate measurements ofthe galaxies LMXB populations. These detection limitsare taken from the papers cited in Table 2 and are inreasonably good agreement with the limits predicted bythe web based simulator pimms (v4.6a) .The X-ray data available for all of these galaxies havepreviously been analyzed and published (see referencesin Table 2). We do not repeat the previous analysis of http://cxc.harvard.edu/toolkit/pimms.jsp these data, but take the X-ray source catalogs (XSCs)for each galaxy from the literature. This includes thequoted source locations and X-ray luminosities ( L x ).For NGC 3379, NGC 4278, NGC 4472 and NGC 4649we take L x as quoted in the papers, for NGC 4594 andNGC 4697 we convert the source counts to L x using theconversions quoted in the papers. For NGC 1399, weconvert the quoted flux in photons/s to L x by compar-ing with the catalog of Liu (2011). Liu (2011) providea catalog of X-ray point sources in 383 nearby galaxies,including all of those considered here. Investigation ofthis catalog showed that it is not as complete as thoseprovided by the individual studies, so it is not used asthe primary dataset for any of the galaxies in our study.However, it does provide a relatively homogeneous cata-log with which to compare the fluxes of sources quotedin each galaxy’s XSCs. This comparison confirms thatthere are no large systematic offsets between the L x val- For NGC 3379, we use higher accuracy RA coordinates thanthe rounded values quoted in the paper. We thank Nicola Brass-ington for providing us with this catalog.
Peacock et al.ues quoted by Liu (2011, in the band 0.3-8 keV) andthose found by the different studies for all galaxies exceptNGC 4472. For NGC 4472, we find that the luminosi-ties from the catalog of Joseph (2013) are fainter thanthose of Liu (2011) and the previous study of Maccaroneet al. (2003, which was based on shallower data). A po-tential reason for this is that Joseph (2013) list sourcefluxes over the narrower 0.5-5keV range. For this study,we use the deeper catalog of Joseph (2013), but scale thequoted L x by 1.4 to match those quoted by Maccaroneet al. (2003) and Liu (2011).We restrict our analysis of each galaxy to inside the r ext ellipse (as defined in Table 1). This ellipse definesthe distance to which the galaxy’s light can be extrapo-lated in 2MASS observations of the galaxy (taken fromthe 2MASS LGA, Jarrett et al. 2003). Field LMXBsmay reside at greater distances than this from the cen-ter of some of these galaxies. However, the ratio of fieldsources to background and GC sources becomes very lowat these larger distances. We also restrict our study to re-gions outside the central regions (given by r inner in Table1). Inside of this region source confusion and gas emis-sion can effect the reliability and detection limits of theXSCs. It is also harder to reliably associate X-ray sourceswith optical counterparts in these inner regions (wherethe density of both is very high). For NGC 4594, werestrict our analysis to the region outside of an inner el-lipse in which the dust lane makes association with opti-cal counterparts less reliable. For NGC 4649, we removean additional region which covers X-ray sources withinthe D25 ellipse of the nearby galaxy NGC 4647. Thisis the same region that was excluded from the galaxy’sXSC by Luo et al. (2013). The field LMXB populationin a galaxy has been observed to trace its stellar emis-sion (e.g. Kundu et al. 2007), hence removing regionsfrom these galaxies should not influence our results. Thefraction of each galaxy’s K-band light that is covered byour study (relative to the total within r ext ) is quoted inTable 2. This was calculated directly from the 2MASSLGA images of each galaxy by masking out the regionsinside r inner , outside of r ext , and those regions that arenot covered by HST observations (which are importantfor removal of non field LMXBs from the XSCs, as dis-cussed below).
Optical counterparts
For all galaxies, the XSCs used include all sources de-tected. They therefore include not only the population ofLMXBs associated with the field of these galaxies (whichis desired for this study), but also background AGN andLMXBs located in GCs. Because all of the galaxies havevery low levels of star formation, the presence of highmass X-ray binaries in the galaxies should be negligible.It is well established that a large fraction (20-70%) ofthe LMXBs in these galaxies are located in GCs (e.g.Angelini et al. 2001; Kundu et al. 2002; Jord´an et al.2004). These LMXBs are likely formed via dynamicalinteractions (e.g. Clark 1975; Jord´an et al. 2007; Peacocket al. 2010). The formation of LMXBs through dynam-ical processes increases with the stellar density, ρ (e.g.Fabian et al. 1975). Formation through these mecha-nisms is therefore dominant in the cores of GCs, whichhave extremely high stellar densities, but insignificant inthe fields of these galaxies, where the stellar density is orders of magnitude lower (see e.g. Fabian et al. 1975;Verbunt & Hut 1987). Thus the GC LMXB populationrepresents a different origin from the field LMXBs. Toobtain reliable field populations, it is therefore vitallyimportant to remove the GC LMXBs from our analysis.To remove X-ray sources associated with GCs (andbackground galaxies), we restrict our study to regions ofthese galaxies that have HST /ACS photometry, and re-move sources with optical counterparts. At the distancesof these galaxies, the
HST observations have z-band de-tection limits 3-4 magnitudes fainter than the peak ofthe GC luminosity function (GCLF; which peaks in thez-band at around -8.5, e.g. Villegas et al. 2010). Sincethe GCLF extends to about 3-4 magnitudes fainter thanthis peak, we detect all but the very faintest GCs. Fur-thermore, LMXBs are primarily found in brighter, moremassive GCs (e.g. Kundu et al. 2003; Kim et al. 2006).We therefore expect to detect the optical counterpart toall of the GC LMXBs. The data used for each galaxyare listed in Table 2. For all galaxies except NGC 4472and NGC 7457,
HST /ACS mosaics are available thatcover the vast majority of the galaxy out to r ext . ForNGC 4472, we cover a smaller fraction of the galaxy lightby using only the three ACS fields that are available forthe galaxy. For NGC 7457 only two pointings, takenwith the wide field planetary camera 2 (WFPC2), areavailable - although these cover all of the detected X-raysources.The HST /ACS images were taken from the HLA , ifavailable, or the MAST archive, otherwise. We use thepipeline reduced and drizzle combined products that areprovided by these archives. Background light, associ-ated with the field stars in the galaxies, was subtractedfrom these images using a ring median filter using the iraf task rmedian with an inner radius of 30 pixels.The world coordinate system (WCS) of the images wasthen aligned relative to the XSCs using the iraf task tfinder . This was done interactively under the taskby matching X-ray sources to likely counterparts in theimages. Because a large fraction of the sources are asso-ciated with GCs or background galaxies, enough sourceswith optical counterparts were present in each ACS fieldto align its WCS to that of the relevant XSC’s.Sources were identified and measured in these back-ground subtracted and WCS aligned ACS images using Sextractor (Bertin & Arnouts 1996). This was runwith a detection threshold of 3 σ and using the associ-ated weight images (the ‘WHT’ images produced by thepipeline) to estimate the noise for each pixel in the sci-ence image. For all galaxies except NGC 1399, a redand blue filter was available for each field. We use theredder band as our primary source catalog and matchsources to the bluer band where detected. Photometrywas obtained through a 0.25 ′′ aperture and calibratedto the AB system using the standard calibration, as de-scribed in the ACS data handbook (Gonzaga et al. 2013).Our primary interest in finding the colors of sources is We note that there is tentative evidence for some dynamicalformation of LMXBs in the very central region of M 31 (Voss &Gilfanov 2007). However, this would make only a small contri-bution to the total LMXB population in the galaxy and, in thispaper, we exclude these central regions from our analysis. http://hla.stsci.edu/ http://archive.stsci.edu/hst/ esting for variability in the IMF at high stellar masses 5 N x ( > L x ) L x /10 [erg/s] field lmxbsGC lmxbsbackgroundKim et al. (2007) Fig. 1.—
The cumulative X-ray luminosity function (XLF) offield LMXBs (solid-red line), GC LMXBs (dashed-blue line) andbackground X-ray sources (dotted-green line) in NGC 4594. Theblack dashed line indicates the 90% completeness limit for these X-ray observations. Also plotted is the prediced XLF of backgroundX-ray sources from Kim et al. (2007). to identify GCs in the galaxies. These clusters should bemarginally resolved. We therefore produced an empiri-cal aperture correction for the 0.25 ′′ aperture using theratio of fluxes of bright sources through a 0.25 ′′ and a0.5 ′′ aperture. The fluxes were then further corrected forlosses from 0.5 ′′ aperture to infinity assuming the aper-ture losses of a point source, as quoted by Sirianni et al.(2005). Finally, the sources were derredened using theGalactic extinction maps of Schlegel et al. (1998).Within our final optical catalog, sources are flagged asGC candidates based on (1) having colors in the range0 . < g − z < . . < B − r < . − . < z < − . − . < r < − . Sextractor stellarity flag < ′′ and 0.5 ′′ apertures of m . − m . > .
4; (4) being nottoo extended to be a GC, m . − m . < .
0. For NGC1399, for which we have only one filter, GC candidatesare selected based on criteria 2-4 only. In addition toGCs, some of the galaxies in our sample may host a fewUCDs (see e.g. Ha¸segan et al. 2005), some of which areknown to host LMXBs (Dabringhausen et al. 2012). Ifpresent, most of these compact galaxies will be includedin our rather broad GC selection criteria, which includessources up to luminosities of L z ∼ . × L ⊙ (assum-ing M z, ⊙ =4.51, Sivakoff et al. 2007). For this paper, thedistinction between UCDs and bright GCs is less impor-tant than ensuring that we detect and remove them fromour sample of LMXBs in the fields of the galaxies. Giventheir bright magnitudes, all UCDs that are present willbe reliably detected and removed from our analysis.Optical counterparts to the X-ray sources in thesegalaxies were identified in these optical catalogs usingtheir calibrated WCS locations. This was done using the software topcat/stilts (Taylor 2006). We exper-imented with different matching radii and found that amatching radius of 0.6 ′′ detected most real counterpartswhile producing few random false matches. The num-ber of random false matches present was estimated byshifting our source catalog by ± ′′ in RA and DEC andaveraging the number of matches found. This predicts 3-7 false matches in the galaxy catalogs, corresponding to ∼
5% of the matches being potentially spurious. Usinglarger matching radii did not increase the number of de-tected sources by significantly more than predicted fromrandom matches. We split the matched sources in to GCLMXBs and other counterparts (background galaxies orforeground stars). Previous work has already searchedfor GC counterparts to the X-ray sources in some of thefields covered by our study. We find good agreementwith these previous identifications. The other matchedsources are assumed to be background AGN and their X-ray luminosity function (XLF) for each galaxy was foundto be in good agreement with that observed in other fieldsby Kim et al. (2007, using their ‘broad bandpass’ rela-tionship). At fainter luminosities we identify fewer AGNsources than predicted. However, this corresponded wellwith the detection limits of these data. We therefore be-lieve that we directly identify (and remove from our lateranalysis) the majority of GCs and background AGN.As an example of the X-ray populations in these galax-ies, we show in Figure 1 the XLF of the field LMXB(solid-red line), GC LMXB (dashed-blue line) and back-ground X-ray source (dotted-green line) populations inNGC 4594. As discussed above, the background pop-ulation (those X-ray sources with non-GC like opticalcounterparts) is in good agreement with that expectedfrom the study of Kim et al. (2007). The figure alsohighlights the well-known result that early-type galaxiestypically have similar numbers of GC and field LMXBs(e.g. Angelini et al. 2001; Kundu et al. 2007).The X-ray sources that are confirmed to have no opti-cal counterparts represent the population of LMXBs inthe field of these galaxies. This is the population weconsider in the subsequent analysis. The final numbersof field LMXBs (and GC LMXBs/background sources)that are identified in each galaxy are listed in Table 2. FIELD LMXB POPULATIONS
The field LMXB XLF of these galaxies
The matching process discussed in Section 2.2 resultsin a clean population of field LMXBs in each of the galax-ies in our sample. Figure 2 shows the cumulative X-rayluminosity function for these field LMXBs in seven ofthe galaxies studied. In this figure, n x is the number ofLMXBs (N x ) scaled by the K-band light ( L K ) covered,such that n x = N x / ( L K × L K ⊙ ). It can be seen thatthe flattening at the faint ends of the XLFs is in goodagreement with the completeness limits quoted in Table2. Figure 2 shows that the field LMXB XLF is remarkablysimilar among these galaxies, both in terms of shape andnormalized number of sources. The one possibly differentgalaxy, NGC 3379, is discussed further below. In addi-tion to plotting the stellar-light normalized XLFs, we canalso compare them to analytical forms for the XLF. Sig-nificant literature is devoted to fitting functional forms Peacock et al. n x ( > L x ) L x /10 [ergs -1 ] NGC4472 NGC4649 NGC1399 NGC4594 NGC4697 NGC4278 NGC3379Broken PL Fig. 2.—
The XLF of field LMXBs in our sample of galaxies, n x ( > L x ) = N x /L K ( > L x ). The number of X-ray sources in eachgalaxy is scaled by the K-band luminosity covered ( L K ). Theblack line shows the broken power-law as described by Equation2, scaled to fit NGC 4278. It can be seen that both the shape ofthe XLF and normalized number of sources is remarkably similarfor most of the galaxies. to the XLFs of galaxies (including those in our sample)and we do not repeat this previous analysis. Two func-tions are generally used to represent a galaxy’s XLF. Thefirst is a simple power-law of the form: N ( > L x ) ∝ L − αx (1)This single power-law, with an exponent α =2.0, haspreviously been found to represent the bright end of theXLF ( L x > ) relatively well (e.g. Humphrey & Buote2008). However, for these galaxies, where the deep Chan-dra observations allow the XLF to be studied to fainterluminosities than are often possible, this single power-law poorly represents the observed XLFs. The XLF isfound to be much flatter at lower L x and we find muchbetter agreement with a broken power-law of the form: N ( > L x ) ∝ (cid:26) ( L x /L b ) − α , if L x > L b . ( L x /L b ) − α , otherwise . (2)where L b is the break luminosity between the two power-laws. Humphrey & Buote (2008) have previously fitsuch a model to a range of early type galaxies (includingthose studied here) and found that a broken power-lawwith L b =2.2 × ergs − , α =2.84 and α =1.4 providesa good representation of the different galaxy’s XLFs. Weplot this function, scaled to fit NGC 4278’s XLF, in Fig-ure 2. It can be seen that Equation 2 represents thehigh completeness regions of the different galaxies XLFsrelatively well. For the two deepest XLF’s, those ofNGC 3379 and NGC 4278, there are suggestions that theXLF flattens slightly at around 1 − × ergs − . Whilea flatter power-law at these faintest luminosities may be n x ( L x > x e r g s - ) S NNGC3379
Fig. 3.—
Normalized number of LMXBs ( n x ) with L x > ergs − , as a function of globular cluster specific frequency(S N ). The dashed line represents a constant n x fit to all galax-ies except NGC 3379. It can be seen that the data are in goodagreement with a fixed n x . This suggests that NGC 3379 is anoutlier from the other galaxies, rather than following a trend withS N . genuine, consideration of this is beyond the scope of thispaper. This is because we only consider X-ray sourceswith L x > × ergs − in the subsequent analysis.Notable from Figure 2 is that, at all luminosities, n x is remarkably similar between the different galaxies –with the possible exception of NGC 3379, which has lesssources, particularly at high L x . The reason for this sin-gle outlier remains uncertain. We note that the color ofthis galaxy is similar to the other galaxies in our sampleand it is thought to have a similarly old age, suggestingthe low n x is not a stellar population effect. Also, asdiscussed in Section 4, the proposed variations in IMFwith galaxy mass, should result in this galaxy having alarger, not smaller, number of LMXBs.A previously proposed explanation for NGC 3379’s low n x is based on the only obvious difference between thisand the other galaxies, its relatively low number of GCs.This could result in a lower number of field LMXBs ifa significant fraction of these were either ejected fromGCs or formed in a GC that was subsequently disrupted.Because GC LMXBs represent a population of LMXBsthat is unrelated to the evolution of the field popula-tion, it is important to consider whether such a popu-lation is significant. Kim et al. (2009) suggested a re-lationship between n x and the GC specific frequency,S N = N GCs × . M V +15) based on three galaxies:NGC 3379, NGC 4278 and NGC 4697. In a larger sam-ple of early type galaxies, Irwin (2005) found no evidencefor such a correlation in their data. Our sample of con-firmed field LMXBs allows us to test for such a relation-ship based on larger samples of galaxies and LMXBs.In Figure 3, we plot n x ( L x > ergs − ) as a functionof S N for all eight galaxies in our sample. The S N foreach galaxy are taken from Ashman & Zepf (1998) for allgalaxies except NGC 7457 (which we take from Hargiset al. 2011). It can be seen that there is little evidencefor a trend between n x and S N and, with the exceptionof NGC 3379, the data are in excellent agreement witha constant n x . Additionally, a number of other obser-vations suggest that the majority of field LMXBs haveesting for variability in the IMF at high stellar masses 7non GC origins. For example: the LMXB populationof the Milky Way is associated with the Galaxy’s diskrather than its halo population (Liu et al. 2001), indi-cating that it formed in the field and not in GCs; theradial profile of field LMXBs in a sample of early typegalaxies has been observed to trace the I-band light pro-file better than the GC profile, suggesting a primordialfield origin (Kundu et al. 2007); also there is evidenceof differences in the XLFs of GC and field LMXB popu-lations (Voss et al. 2009; Zhang et al. 2011), suggestingdifferent origins. These indicate that the contaminationfrom non-primordial LMXBs in these galaxies is likely tobe negligible. The normalized number of field LMXBs
In Figures 4 and 5, we show how n x varies as a functionof a galaxy’s velocity dispersion ( σ , measured at 1 kpc bythe studies referenced in Table 1) and total K-band lumi-nosity ( L K , from the 2MASS LGA, Jarrett et al. 2003).We consider n x down to two different X-ray limits. Thebottom panels show the bright X-ray sources in eachgalaxy, those with L x > ergs − (hereafter, n x, ).The X-ray populations for all of the galaxies should becomplete to this limit and therefore require no assump-tions about the XLF. However, this limit only considersthe brightest end of the XLF and therefore includes onlya small fraction of the total LMXB population. This isa particular issue for the lower luminosity galaxies whichonly have a small number of sources above this limit. Inorder to take advantage of the deeper detection limits forsome of the galaxies, we plot in the top panels of Figures4 and 5 the number of LMXBs with L x > × ergs − (hereafter, n x, ). For NGC 3379 and NGC 4278, theXLFs should be complete to this limit. For the othergalaxies we extrapolate their LMXB population by as-suming the universal broken power-law XLF discussedin Section 3.1 and fitting it to the galaxies XLF aboveits detection limit. The LMXB population to this limittherefore has improved statistics for some of the galaxiesbut, for others, it is more susceptible to systematic er-rors due to extrapolating the XLF. We do not quote an n x, for NGC 7457 because its high L x detection limitand low number of sources do not allow us to accuratelyextrapolate its XLF to these lower luminosities. Thenumber of LMXBs as a function of σ and L K is found tobe in good agreement between the two detection limits.Apparent from Figures 4 and 5 is that the normalizednumber of field LMXBs is similar among these galax-ies. We note that this is in agreement with the previousresult of Kundu et al. (2003, see e.g. their Figure 5),who studied a smaller sample of galaxies (NGC 1399,NGC 3115, NGC4365 and NGC 4472). In these figures,we also show the predicted variation in n x for an invari-ant IMF (red-dashed line) and an IMF which becomesincreasingly bottom heavy as a function of galaxy mass(blue-dotted line). It can be seen that the similar n x observed is in better agreement with a fixed IMF than avariable one. In the next section, we discuss these pre-dictions and their consistency with these data. LMXB CONSTRAINTS ON IMF VARIATIONS
In this section, we discuss the influence of a galaxy’sIMF on its LMXB population. Specifically, we predictthe variation in n x , as a function of galaxy mass, for an n x ( L x > x e r g s - ) invariant IMFvariable IMF 0 1 2 31.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 n x ( L x > x e r g s - ) log( σ ) [kms -1 ] Fig. 4.—
Total number of field LMXBs in each galaxy (scaled by L K ) with L x > × ergs − ( n x, , top) and L x > ergs − ( n x, , bottom) as a function of the galaxy’s velocity dispersion( σ ). The number of sources is scaled by the amount of K-bandstellar light covered, such that an invariant IMF among thesegalaxies predicts a constant n x . This case, discussed in Section4.1 is represented by the red dashed line. The blue dotted lineshows the predicted variation of n x with σ assuming that theIMF varies as required to explain the observed M/L ratio trends,as discussed in Section 4.2. It can be seen that the constantIMF model provides a better representation of the data than thevariable IMF model. invariant IMF (Section 4.1) and an IMF that varies sys-tematically with galaxy mass (Section 4.2). We comparethese predictions with the data presented in the previ-ous section and discuss the implications for the inferredIMFs of these galaxies.
An invariant IMF
If the IMF is invariant among all of these galaxies, thenumber of black holes and neutron stars should simplyscale with the mass of the stellar population. One wouldtherefore predict a constant n x as a function of galaxymass. Such a scenario is represented in Figures 4 and5 by the horizontal red dashed line. The formation ofLMXBs in the field of a galaxy is still a relatively poorlyunderstood process, likely involving a period of commonenvelope evolution. Because accurate constraints on thenumber of LMXBs formed in a stellar population arenot available from such theories, we fit the scaling of theline in Figures 4 and 5 to the data. It can be seen that a Peacock et al. n x ( L x > x e r g s - ) invariant IMFvariable IMF 0 1 2 310.0 10.5 11.0 11.5 12.0 n x ( L x > x e r g s - ) log(L K ) [L K O• ] Fig. 5.—
Similar to Figure 4, but showing the number of fieldLMXBs (per L K ) in each galaxy with L x > × ergs − ( n x, , top) and L x > ergs − ( n x, , bottom) as a function ofthe galaxy’s K-band luminosity ( L K ). The red-dashed line showsthe prediction for an invariant IMF. The blue-dotted line showsthe expected variation in n x , if the IMF varies as a function of L K to explain the observed M/L variation (see Section 4.2 fordetails). It can be seen that the observed n x in these galaxies isin better agreement with the constant IMF prediction. universal number of LMXBs, per unit K-band luminosity,provides a good representation of the data. Running a χ test between n x, and this model we find χ /ν =2.0,which is consistent with the data. For n x, , the smallererror bars suggest a poorer fit with χ /ν =4.3. This isinconsistent with the data with a significance of just over3 σ .It is clear from Figures 4 and 5, that the main outlierfrom the constant n x model is NGC 3379, which has arelatively low number of LMXBs (as discussed above).Rerunning our tests, but excluding NGC 3379, we find χ /ν =0.96 and 0.81 (for n x, and n x, , respectively)– confirming that the other seven galaxies are in excel-lent agreement with the constant IMF model. While thereason for NGC 3379 differing from the other galaxies isstill uncertain, it is unlikely related to the proposed IMFvariations. This is because its relatively low mass shouldproduce more LMXBs under the proposed IMF varia-tions, not fewer as observed. Additionally, NGC 4278and NGC 4697 have quite similar masses to NGC 3379,so a mass dependent IMF would be expected to effect all of these galaxies in a similar way. We note that, evenincluding NGC 3379, the data are only inconsistent (byaround 3 σ ) for n x, . The population of NGC 3379 is bet-ter constrained to this fainter limit, thanks to its relativeproximity and deep observations. However, it should benoted that (with the exception of NGC 4278) the othergalaxies are not complete to this detection limit and sotheir n x s are more susceptible to systematic errors inthe scaling. Clearly it will be important to increase thiswork to larger samples of galaxies and to try to pushtheir XLFs to deeper limits. In the future, larger sam-ples should help to identify whether NGC 3379 is a trueoutlier or whether significant variations in n x are alsopresent in other galaxies. A variable IMF - as a function of galaxy mass
In this section, we predict and test the effect of theproposed IMF variations with galaxy luminosity and ve-locity dispersion on the number of LMXBs in ellipticalgalaxies. To predict the variation with galaxy mass,we note that it is now thought that the proposed IMFvariation must explain the observed
M/L variation withgalaxy mass, as observed in the fundamental plane (Cap-pellari et al. 2012). Below, we briefly review the fun-damental plane of elliptical galaxies and the observed
M/L variations with galaxy parameters before calculat-ing the required IMF variation and resulting variationin the number of black holes (BHs) and neutron stars(NSs).One of the key features of elliptical galaxies is thatthey have a very tight relation between their veloc-ity dispersion, effective radius and surface brightness: R e ∝ σ . I − . e , known as the “fundamental plane”(Dressler et al. 1987; Djorgovski & Davis 1987). It hasbeen known since the discovery of the fundamental planethat the observed scaling between velocity dispersion andthe parameters relating to the effective radius and sur-face brightness for early-type galaxies deviates from thatexpected from the Virial theorem. This deviation is suchthat the M/L for early-type galaxies increases systemat-ically with increasing galaxy mass, luminosity, and veloc-ity dispersion. Many studies have quantified this trend(see e.g. the recent comprehensive work by Graves &Faber 2010, and references therein), finding for example(
M/L ) V ∝ σ . (Graves & Faber 2010), ( M/L ) r ∝ σ . (Cappellari et al. 2013), ( M/L ) V ∝ L . V (Mobasheret al. 1999), and ( M/L ) K ∝ L . K (e.g. Pahre et al.1998; Mobasher et al. 1999; La Barbera et al. 2010).Importantly, these trends are all much larger than canbe accounted for by the known stellar populations dif-ferences among early-type galaxies. Specifically, manystudies over the years have investigated the role increas-ing metallicity with increasing galaxy luminosity. As de-scribed in Graves & Faber (2010), this falls far shortof accounting for the increase in M/L with increasing σ . They find that stellar population effects account foronly about one-quarter of the observed trend, and thatthe remaining “tilt” in the fundamental plane follows M/L ∝ σ . . Additionally, the near-infrared work citedabove is mostly immune to metallicity, so M/L ∝ L . K also describes the mass-to-light trend with metallicity ac-counted for. The long-standing question has been whatcauses this systematic increase in M/L with increasingesting for variability in the IMF at high stellar masses 9early-type galaxy mass, luminosity and velocity disper-sion. Moreover, because the fundamental plane is verynarrow, whatever the cause, it must work very system-atically across the range of early-type galaxies.Two possible mechanisms are commonly presented toaccount for the tilt of the fundamental plane. The first,is that higher velocity dispersion early-type galaxies mayhave systematically larger fractions of dark matter in theinner regions measured at an effective radius or so. Thealternative explanation is that the IMF may vary, withhigher luminosity and larger velocity dispersion early-type galaxies having a systematically larger
M/L ratiobecause of systematic changes in the IMF. These possi-bilities are outlined in many papers (e.g. Renzini & Ciotti1993; Zepf & Silk 1996; Treu et al. 2010; Graves & Faber2010; Cappellari et al. 2012). It was recently argued byCappellari et al. (2012) that dark matter variations cannot explain the observations. If this is the case, then thetrends observed must be explained by an IMF that variessystematically as a function of galaxy mass.To investigate how the IMF of a galaxy must varyto explain the above
M/L relations, we adopt a modelin which the galaxy’s IMF is a mixture of a standardKroupa IMF and a power-law IMF with x =2.8. Wethen vary the ratio of these components to explainthe observed trends of M/L with velocity dispersionand luminosity. Using the stellar population synthesismodels of Maraston (2005, rerun for a power-law IMFwith x=2.8), for a 10 Gyr simple stellar population withsolar or half solar metallicity, we find that the differencein the K-band
M/L resulting from the different IMFs is: R M/L = (
M/ L K ) . ( M/ L K ) kro = 2 . . (3)This ratio is the same as that used by Cappellari et al.(2012) and is quite insensitive to the exact age and metal-licity of the stellar population. We proceed by first con-sidering the number of NSs and BHs that are producedfrom the evolution of the two IMFs considered. In orderto normalize the two IMFs to the same total mass, weconsider the Kroupa IMF of the form: dMdm = N , kro (cid:26) m × m − . , m > . M ⊙ m × m − . , . M ⊙ < m < . M ⊙ (4)and the power-law IMF with exponent x =2.8: dMdm = N , . × m × m − . (5)The two normalization constants N can then be foundfor each IMF by integrating over the total stellar massrange (0.1-100 M ⊙ ) and normalizing to a total mass of1 M ⊙ . Performing this integration yields N , kro = 0 . N , . = 0 . > M ⊙ : N kro ( M > M ⊙ ) = 0 . Z m − . dm = 0 . N . ( M > M ⊙ ) = 0 . Z m − . dm = 0 . x =2.8 IMF. However, we require this ratio fora constant luminosity population, because we normalizeour data by this easier to observe parameter. We there-fore find that the ratio of BHs and NSs in the Kroupa tothe x =2.8 IMF is: R NS / BH = 0 . . × R M/L = 2 . x =2.8 IMF component has to vary, asa function of σ to explain the observed variation in the M/L ratio,
M/L ∝ σ . (Cappellari et al. 2013). Forgalaxies with low masses, those with σ ∼ − , theirobserved M/L requires that their IMF must be similarto a Kroupa IMF. For galaxies with higher σ , we then in-crease the x =2.8 component so as to match the observedincrease in their M/L ratios. The resulting fraction ofthe IMF composed of the x =2.8 component, F . , as afunction of σ is given by: F . ( σ ) = 1( R M/L − (cid:18) ( M/L ) σ ( M/L ) kro − (cid:19) = 1( R M/L − (cid:18) σ . . − (cid:19) (9)In this way F . =0.0 and the IMF is purely Kroupa, when σ =95 kms − (as defined) and F . =1.0 and the IMF ispurely an x =2.8 IMF, when σ =300 kms − . As an ad-ditional test, we also consider the the variation of F . required to explain the observed relationship between the M/L and L K , M/L ∝ L . K (La Barbera et al. 2010).We again note that galaxies at the low mass end, thosewith luminosities of L K ∼ × L K ⊙ are expected tohave Kroupa like IMFs. Following a similar process usedfor the σ relationship, the fraction of the x =2.8 IMF asa function of L K is found to be: F . ( L K ) = 1( R M/L − (cid:18) L . (1 × ) . − (cid:19) (10)Finally, having found how the ratio of the IMF compo-nents varies as a function of σ and L K , we use equation8 to calculate the resulting variation in the number ofNSs and BHs: N NS / BH ( σ/L K ) N NS / BH (kro) = F . R NS / BH + F kro = 1 − (cid:18) − R NS / BH (cid:19) F . (11)Where we have noted that the fraction of the KroupaIMF, F kro = 1 − F . . This relationship, combined with0 Peacock et al.equations 9 and 10, is used to produce the predicted num-bers of LMXBs as a function of σ and L K in Figures 4and 5 (the blue dotted lines).It can be seen from Figures 4 and 5 that the dataare in poor agreement with these predicted trends. Totest these predictions against the observed number ofLMXBs, we run χ tests between the data and the pre-dicted trends with both σ and L K . The reduced χ statistics obtained for the σ and L K relations to the n x, data are χ /ν =10.5 and χ /ν =9.5, respectively.For the 5 degrees of freedom, the variable IMF modelsare therefore strongly rejected, with a confidence of 6.8 σ and 6.4 σ . Considering the data for only the brightestsources in each galaxy, n x, , we find that, for the six de-grees of freedom, χ /ν =4.5 for σ and χ /ν =3.5 for L K .This is again significantly inconsistent, although the con-fidence is lower due to the larger observational uncertain-ties. Furthermore, we note that even if we exclude thegalaxy NGC 3379 from our fits (which is an outlier fromboth the invariant and variable IMF models), the n x, data are still in much poorer agreement with the variableIMF than the invariant one, with χ /ν =4.8 for σ and χ /ν =2.9 for L K (c.f. χ /ν =0.8 for σ and χ /ν =0.96for L K for an invariant IMF, see Section 4.1). Other effects on the LMXB population
Our goal is to test for IMF variations in early-typegalaxies as a function of their σ and L K by comparingtheir normalized number of field LMXBs. To do this, weneed to consider the potential effect of other propertiesthat vary with σ and L K in these galaxies. One candi-date is metallicity ( Z ), which is well-known to increasewith increasing σ and L K . Fortunately, we can calcu-late the effect of this on the number of LMXBs. Thomaset al. (2010) found that this trend in early-type galaxies issuch that [Z/H]=-1.34+0.65 log ( σ ). Thus over the rangecovered by our sample of galaxies (with detection lim-its, L X > ergs − ), the expected increase in [Z/H] isonly 0.14 dex. Although we do not know the dependenceof field LMXBs on metallicity directly, we do know thedependence within GCs, where the number of LMXBsscales as Z . (Smits et al. 2006; Sivakoff et al. 2007).Thus, the expectation is that the increasing metallicity ofbrighter, higher velocity dispersion galaxies will increasethe LMXB numbers by only about 10%. This falls farshort of the proposed increase due to changing the IMF(which is ∼ σ ). Thus, the ob-served metallicity dependence of elliptical galaxies doesnot effect our analysis.Another property of elliptical galaxies to consider isage. The galaxies in our sample were often selected forX-ray observations because stellar populations studiesindicated that they had a uniformly old age (e.g. Kimet al. 2009). Therefore, age effects would seem to bean unlikely source of variation. However, in a statis-tical sense, lower velocity dispersion galaxies are foundto have slightly younger ages (e.g. Graves et al. 2007;Thomas et al. 2010). Adopting the Thomas et al. (2010)relation between galaxy age and σ , gives an increase inage from about 9 to 11 Gyr as σ increases from 180 to290 kms − (similar ages are also predicted from the re-lation of Graves et al. 2007). We note that there arefew constraints on the variation of LMXB numbers over this range of ages. Therefore, an extremely steep age de-pendence of LMXB formation at these old ages can notbe completely excluded. However, it seems difficult toachieve a large change over such a small range of ages.In particular, to hide the proposed variation in the num-ber of LMXBs due to IMF variations, any such changewould have to be dramatic (a factor 3 or so from around9 to 11 Gyrs) and carefully tuned to decrease with σ toproduce the constant LMXB number observed.Therefore, the comparison of the normalized numberof field LMXBs in different early-type galaxies is a directtest of the ratio of the number of (now evolved) massivestars to the number of approximately solar mass starsthat are now dominating the light in these old galaxies.Our results presented here demonstrate that this ratioappears to be constant for the most part across a widerange of early-type galaxy masses. The simplest varia-tions of the IMF, in which its slope varies with galaxymass, would therefore appear to be ruled out. It is im-portant to emphasize though, that the LMXB test pre-sented here does not directly test the ratio of the slightlyless than solar mass stars currently dominating the lightof early-type galaxies to very low mass stars that con-tribute almost no light. Thus it is possible to constructan IMF variation in which the IMF is invariant for nearlyall masses, but with a varying contribution from verylow mass ( < M ⊙ ) stars. Such a population of verylow-mass stars only would have to have the same spatialdistribution as the “normal” IMF population in order tosatisfy the constraints from dynamics and strong lensingthat mass follows light. Whether such an IMF is physi-cally plausible remains to be seen. However, if one wishesto preserve IMF variations to explain previous work inthe context of this study, a solution of this kind is re-quired. Alternatively, the IMF may not vary, and otherastrophysical explanations of near-infrared line featuresin early-type galaxies may be found. An invariant IMFwould also require new a different explanation for thedynamical observations and some lensing results, suchas returning to dark matter arguments. CONCLUSIONS
In this paper, we use the number of field LMXBs perstellar luminosity to investigate the ratio of the numberof high mass stars ( & M ⊙ ) to low mass stars ( < M ⊙ )that were formed in a sample of local early-type galaxies.We find that the XLFs and normalized number of fieldLMXBs ( n x ) are remarkably similar among the galaxiesobserved.We consider the implications of this result for the IMF,specifically predicting the expectations from an invari-ant IMF and an IMF which becomes increasingly bottomheavy as a galaxy’s mass increases. The latter variation ismotivated as an explanation for the correlation observedbetween the M/L of an early-type galaxy and its σ and L K . We find that the data are more consistent with aninvariant IMF than a variable one. Indeed, we show thatthe data are inconsistent with a situation where galaxyIMFs change from a Kroupa IMF for low mass galaxiesto an IMF which is the sum of a Kroupa plus an x =2.8power-law for higher mass galaxies. We conclude thatthere is no evidence in the LMXB populations of thesegalaxies for the ratio of high mass stars increasing withdecreasing galaxy mass. Such a correlation would haveesting for variability in the IMF at high stellar masses 11been expected under the previously proposed IMF vari-ations that were invoked to explain the observed spectraand dynamics of these galaxies.We note that one galaxy in our sample of eight,NGC 3379, is also inconsistent with a fixed IMF. Whilewe can not identify a reason for the relatively low numberof sources in this galaxy, we note that systematic IMFvariations with mass can not explain it. This galaxyhighlights the need to extend this work to larger sam-ples of galaxies. This will be possible with new anddeeper Chandra observations of more galaxies. Addition-ally, new
HST mosaics of nearby early-type galaxies thathave
Chandra data will allow us to study larger regions ofthe galaxies. Particularly important will be new
Chandra data for galaxies in the low mass range, where IMF effectsshould be largest and produce relatively large numbersof LMXBs. Additionally, deeper data for NGC 7457 willallow us to more accurately constrain its LMXB popula-tion.
ACKNOWLEDGMENTS
We thank the anonymous referee of this paper for care-ful consideration and providing detailed comments thatwere beneficial to the final version. We thank TanaJoseph for providing us with a copy of her catalog ofX-ray sources in NGC 4472, Nicola Brassington for pro-viding us with an original copy of her catalog of X-raysources in NGC 3379 and Jay Strader for helpful discus-sions related to this paper. We also thank Charlie Con-roy, Pieter van Dokkum, Ignacio Ferreras, Pavel Kroupaand Russell Smith for helpful comments on the arXive-print version of this paper.MBP and SEZ acknowledge support from NASAthrough the ADAP grant NNX11AG12G and throughthe Chandra award AR4-15007X. AK acknowledges sup-port for this work provided by NASA through Chandraawards GO0-11111A and AR1-12009X.This research has made use of NASA’s AstrophysicsData System.
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